Based on his revelations in Ch. 31, I can imagine him being somewhat indulgent as a father, and yet tending toward being overprotective at times. Indulgent because it sounds like he lost his mother at a young age and his father was not much of a parent, so he would want to make up for that and overprotective because of what happened to Eliza and how that might have been avoided had he not allowed her to go to Bath.